There are 100 students ( 75 speak English, 83 of them speak German, 10 of them don't speak any language) How many of this students speak two languages.
Answers (4)
10 students don't speak any language. From 100 students this leaves 90.
83 - (90 - 75) = 68
or if we start with the English speakers
75 - (90 - 83) = 68
68 students speak two languages.
You have to identify the intersection (or the overlap) between the two sets of students.
0.......7............................................75................90..........100
|--------- eng = 75 ------------------------|
..........|------------- ger = 83 -----------------------------|
..........|---------- overlap = 68 ----------|
The overlap of [7,75[ = 75 - 7 = 68 is the solution.
My little diagram serves just to help visualise the idea but with the quite limited means of this editor it's obviously not true to scale.
Let The Number Of students who speak English be n(A)
Let The Number Of students who speak German be n(B)
Therefore, n(A) = 75 and n(B) = 83
Total Number of Students are :- n(A union B) = 110
But ten students speak neither English Nor German
So, total no. of students = 110 - 10 = 100
By Identity,
n(A union B) = n(A) + n(B) - n(A intersection B)
Therefore, 100 = 75 + 83 - n(A intersection B)
Therefore, - n(A intersection B) = 100 - 158
Therefore, - n(A intersection B) = - 58
Therefore, n(A intersection B) = 58
So, The Number Of Students who Speak Both The Languages are 58
10 students don't speak any languages, so from 100 students this leaves 90. And this means that students who speak English, students who speak German, and students who speak English and German must be 90 in total. Suppose that 58 is the correct answer, so: students who 'only' speak English is 17, and students who 'only' speak German is 25. Then, let's add: 17 + 58 + 25 = 100. And the answer is not 90 and it is wrong!
Suppose that 68 is the correct answer, so: students who 'only' speak English is 7, and students who 'only' speak German is 15. Then let's add: 7 + 68 + 15 = 90. And the answer is 90 and it is correct!
So the answer is 68 students who speak two languages.
There is a total of 100 students given, not a total of 110.
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Answer:
Let The Number Of students who speak English be n(A)
Let The Number Of students who speak German be n(B)
Therefore, n(A) = 75 and n(B) = 83
Total Number of Students are :- n(A union B) = 110
But ten students speak neither English Nor German
So, total no. of students = 100 - 10 = 90
Thus we have
n(A union B) = n(A) + n(B) - n(A intersection B)
Therefore, 90 = 75 + 83 - n(A intersection B)
Therefore, - n(A intersection B) = - 68
Therefore, n(A intersection B) = 68.
As I wrote above. ;-)